Drop[list, {m, n, k}] returns list with objects m through n in increments of k deleted. DSolve[equation, y[x], x] gives the general solution, y[x], of the differential equation, equation, whose independent variable is x. DSolve[equation, y, x] gives the general solution, y, of the differential equation expressed as a pure function within a list. ReplaceAll (/.) may then be used to evaluate the solution. Alternatively, one may use Part or [[ ]] to extract the solution from the list. Dt[f[x, y]] returns the total differential of f[x, y]. Dt[f[x, y], x] returns the total derivative of f[x, y] with respect to x. E or is the base of the natural logarithm. Eigensystem[matrix] returns a list of the form {eigenvalues, eigenvectors}. Eigenvalues[matrix] returns a list of the eigenvalues of matrix. Eigenvectors[matrix] returns a list of the eigenvectors of matrix. Eliminate[equations, variables] eliminates variables from a set of simultaneous equations. Equal[x, y] or x y is True if and only if x and y have the same value. EulerGamma is Euler s constant and is approximately 0.577216. It has applications in integration and asymptotic expansions. Exp[x] is the natural exponential function. Other equivalent forms are E^x and Ex. Lowercase e cannot be used, but the special symbol from the Basic Math Input palette may be used instead. Exponential functions to the base b are computed by b^x or bx. Expand[poly] expands products and powers, writing poly as a sum of individual terms. ExpandAll[expression]expands both numerator and denominator of expression, writing the result as a sum of fractions with a common denominator. ExpandDenominator[expression] expands the denominator of expression but leaves the numerator alone. ExpandNumerator[expression] expands the numerator of expression but leaves the denominator alone. ExpToTrig[expression] converts exponential functions to trigonometric and/or hyperbolic functions. Factor[poly] attempts to factor poly over the integers. If factoring is unsuccessful, poly is unchanged. Factorial[n] or n! gives the factorial of n if n is a positive integer and (n + 1) if n has a noninteger positive value. FactorInteger[n] gives the prime factors of n together with their respective exponents. FactorTerms[poly] factors out common constants that appear in the terms of poly. FactorTerms[poly, var] factors out any common monomials containing variables other than var. Fibonacci[n] returns the nth Fibonacci number. FindMaximum[f[x], {x, x0}] finds the relative maximum of f(x) near x0. FindMinimum[f[x], {x, x0}] finds the relative minimum of f(x) near x0. FindRoot[lhs rhs, {x, x0}] solves the equation lhs = rhs using Newton s method with starting value x0. FindRoot[lhs rhs,{x, {x0, x1}] solves the equation lhs = rhs using (a variation of) the secant method with starting values x0 and x1. FindRoot[lhs rhs,{x, x0, xmin, xmax}] attempts to solve the equation, but stops if the iteration goes outside the interval [xmin, xmax]. FindRoot[equations, {var1,a1},{var2,a2},...] attempts to solve equations using initial values a1, a2, . . . for var1, var2, . . . , respectively. The equations are enclosed in a list: {equation1,equation2,...}. Alternatively, the equations may be separated by && (logical and). First[list] returns the element of list in the first position. Flatten[list] converts a nested list to a simple list containing the innermost objects of list. Flatten[list, n] flattens a nested list n times, each time removing the outermost level. The depth of each level is reduced by n or to a minimum level of 1. FlattenAt[list, n] flattens the sublist that is at the nth position of the list by one level. If n is negative, Mathematica counts backward, starting at the end of the list.

Floor[x] returns the greatest integer which does not exceed x. This is sometimes known as the greatest integer function and is represented in many textbooks by x . For[initialization, test, increment, expression] executes initialization, then repeatedly evaluates expression, increment, and test until test becomes False. FractionalPart[x] gives the fractional portion of x (decimal point included). FullForm[expression] exhibits the internal form of expression. FullSimplify[expression] tries a wide range of transformations on expression involving elementary and special functions, and returns the simplest form it finds. Function[x, body] is a pure function with a single parameter x. Function[{x1, x2,...}, body] is a pure function with a list of parameters x1, x2,... GCD[m, n] returns the greatest common divisor of m and n. GoldenRatio has the value (1 + 5 ) / 2 and has a special significance with respect to Fibonacci series. It is used in Mathematica as the default width-to-height ratio of two-dimensional plots. Graphics[primitives]creates a two-dimensional graphics object. Graphics3D[primitives] creates a three-dimensional graphics object. GraphicsArray[{g1, g2, ...}] plots a row of graphics objects. GraphicsArray[{g11, g12, ...},{g21, g22, ...}}] plots a two-dimensional array of graphics objects. Greater[x, y] or x > y is True if and only if x is numerically greater than y. GreaterEqual[x, y] or x >= y or x y is True if and only if x is numerically greater than y or equal to y. HankelMatrix[n, list] creates a Hankel matrix whose first row (and column) is list. HankelMatrix[n] creates a Hankel matrix whose first row (and column) is {1, 2, 3,..., n}. HeavisideTheta[x] returns a value of 0 if x < 0 and 1 if x > 0. HilbertMatrix[m, n] creates an m n Hilbert matrix. HilbertMatrix[n] creates an n n Hilbert matrix IdentityMatrix[n] creates an n n identity matrix. IdentityMatrix[n] produces an n n matrix with 1s on the main diagonal and 0s elsewhere. If[condition, true, false] evaluates condition and executes true if condition is True and executes false if condition is False. If[condition, true, false, neither] evaluates condition and executes true if condition is True, executes false if condition is False, and executes neither if condition is neither True nor False. If[condition, true] evaluates condition and executes true if condition is True. If condition is False no action is taken and Null is returned. If[condition,, false] evaluates condition and executes false if condition is False. If condition is True no action is taken and Null is returned. (Note the double comma.) Implies[p, q] or p q is False if p is True and q is False; True otherwise. Increment[x] or x ++ increases the value of x by 1 but returns the old value of x. Infinity or is a constant with special properties. For example, + 1 = . InputForm[expression] prints expression in a form suitable for input to Mathematica. Insert[list, x, n] returns list with x inserted in position n. Insert[list, x, n] returns list with x inserted in the nth position from the end. Insert[list, x,{m, n}] returns list with x inserted in the nth position of the mth entry in the outer level. IntegerPart[x] gives the integer portion of x (decimal point excluded). Integrate[f[x], x] computes the antiderivative (indefinite integral) f ( x ) dx. b Integrate[f[x], {x, a, b}] computes, whenever possible, the exact value of f ( x ) dx. a The symbol on the Basic Math Input palette may be used as well. Integrate[f[x, y], {x, xmin, xmax}, {y, ymin, ymax}] evaluates the double integral Integrate[f[x, y, z], {x, xmin, xmax}, {y, ymin, ymax}, {z, zmin, zmax}] evaluates the triple integral